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Definitions

• the present invention relates to a method and apparatus for encoding and decoding a video signal and, more particularly, to a coding technology using an additional control of qunatization error.
• Compression coding means a set of signal processing technologies for sending digitalized information through a communication line or storing digitalized information in a form suitable for a storage medium.
• Media such as videos, images, and voice may be the subject of compression coding.
• video compression a technique for performing compression coding on videos.
• a hybrid coding technology includes spatially predicting samples using previously decoded context values and performing transform coding on predicted errors. Such a process is performed on a Gaussian signal so that it has an optimized a Rate Distortion (RD) value.
• RD Rate Distortion
• An embodiment of the present invention is directed to more efficiently coding a signal having an edge and directional structure.
• An embodiment of the present invention is directed to non-casually predicting a video signal using a transform-coded signal together with a predicted signal.
• An embodiment of the present invention is directed to coding a video signal based on non-orthogonal transform.
• An embodiment of the present invention is directed to obtaining an optimized transform coefficient that minimizes distortion.
• An embodiment of the present invention is directed to deriving a Rate Distortion (RD) -optimized quantization step size.
• An embodiment of the present invention is directed to representing a non-casual coding technology to which the present invention may be applied using non-orthogonal transform having a form and parameters.
• An embodiment of the present invention is directed to controlling a quantization error in both a space domain and a frequency domain.
• An embodiment of the present invention is directed to defining different diagonal matrices in order to differentiate the importance of errors on the space domain.
• An embodiment of the present invention is directed to proposing a method of calculating optimized diagonal matrices from a viewpoint of Rate Distortion (RD) .
• RD Rate Distortion
• An embodiment of the present invention is directed to proposing a method of more finely controlling a quantization error on the space domain.
• the present invention proposes a method of more efficiently coding a signal having an edge and directional structure .
• the present invention proposes a method of non-casually predicting a video signal using a transform-coded signal together with a predicted signal.
• the present invention proposes a method of coding a video signal based on non-orthogonal transform.
• the present invention proposes a quantization algorithm for obtaining an optimized transform coefficient .
• the present invention proposes a method of deriving an optimized quantization step size.
• the present invention proposes a non-casual coding technology that may be represented by non-orthogonal transform having a form and parameters.
• the present invention proposes a method of generating an optimized prediction signal using all the already reconstructed signals and a context signal.
• the present invention proposes a method of controlling a quantization error in both a space domain and a frequency domain.
• the present invention defines different diagonal matrices in order to differentiate the importance of errors on the space domain.
• the present invention proposes a method of calculating optimized diagonal matrices from a viewpoint of Rate Distortion (RD) .
• the present invention proposes a method of more finely controlling a quantization error on the space domain.
• the present invention can perform more elaborate and advanced prediction using all the decoded information.
• the present invention can code a signal having an edge and directional structure more efficiently by non-casually predicting a video signal using a transform-coded signal together with a predicted signal.
• the present invention can perform more elaborate and advanced prediction by proposing a non-casual coding technology that may be represented by non-orthogonal transform having a form and parameters.
• the present invention can minimize a quantization error by proposing a quantization algorithm for obtaining an optimized transform coefficient.
• the present invention can perform more advanced coding by proposing a method of deriving an optimized quantization step size.
• the present invention can generate an optimized prediction signal using all the already reconstructed signals and a context signal.
• FIGS. 1 and 2 are schematic block diagrams of an encoder and a decoder in which video coding is performed;
• FIGS. 3 and 4 illustrate embodiments to which the present invention may be applied and are schematic block diagrams of an encoder and a decoder to which an advanced coding method has been applied;
• FIGS. 5 and 6 illustrate embodiments to which the present invention may be applied and define layers illustrating a method of performing prediction using previously coded pixels
• FIG. 7 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a method of performing prediction using previously coded pixels for each layer;
• FIG. 8 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a quantization process for obtaining an optimized coefficient
• FIG. 9 illustrates an embodiment to which the present invention may be applied and is a detailed flowchart illustrating a quantization process for obtaining an optimized coefficient
• FIG. 10 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a process of obtaining an optimized quantization step size
• FIGS. 11 and 12 illustrate embodiments to which the present invention may be applied, wherein FIG. 11 illustrates test images to which the present invention has been applied and FIG. 12 illustrates percentages of rate gains to test images ;
• FIG. 13 illustrates an embodiment to which the present invention may be applied and is a schematic flowchart illustrating an improved predictive coding method
• FIG. 14 illustrates an embodiment to which the present invention may be applied and is a schematic flowchart illustrating a method of performing quantization based on an optimized quantization step size
• FIGS. 15 and 16 illustrate embodiments to which the present invention may be applied and are schematic block diagrams of an encoder and a decoder to which an advanced coding method has been applied through control of a quantization error;
• FIG. 17 illustrates an embodiment to which the present invention ' may be applied and is a flowchart illustrating a process of obtaining a scaling diagonal matrix through a Rate Distortion (RD) optimization process;
• RD Rate Distortion
• FIG. 18 illustrates an embodiment to which the present invention may be applied and is a graph illustrating a comparison between the coding gains of respective images in the case in which coding is performed using an optimized scaling matrix and the case in which coding is performed using an existing method
• FIGS. 19 and 20 illustrate embodiments to which the present invention may be applied and are schematic block diagrams of an encoder and a decoder to which an advanced coding method has been applied;
• FIG. 21 illustrates an embodiment to which the present invention may be applied and is a schematic flowchart illustrating an advanced video coding method.
• An embodiment of the present invention provides a method of encoding a video signal, comprising receiving an original video signal; comparing the original video signal with a previously reconstructed signal; generating a correction signal to minimize a sum of a distortion component and a rate component; and entropy-encoding the correction signal that is transmitted to the decoder for video signal reconstruction, wherein the previously reconstructed signal has been inverse- transformed by additionally using a scaling diagonal matrix.
• the correction signal is generated based on another diagonal matrix being used to differentiate a weighting of errors in a spatial domain.
• the method further includes calculating an optimal set of multiple diagonal matrices including the scaling diagonal matrix, wherein the correction signal is generated based on the optimal set of multiple diagonal matrices.
• the optimal set of multiple diagonal matrices is encoded as side information, and is transmitted to a decoder.
• the optimal set of multiple diagonal matrices is encoded before encdoing frames of the original video signal.
• the distortion component is indicative of total distortion between the original video signal and a reconstructed signal
• the rate component is indicative of a number of bits required to send a quantized coefficient
• Another embodiment of the present invention provides a method of decoding a video signal, comprising: receiving the video signal including a correction signal; reading side information including multiple diagonal matrices from the video signal; obtaining the correction signal by entropy- decoding the video signal; and reconstructing a signal based on the correction signal and the multiple diagonal matrices.
• the multiple diagonal matrices includes a scaling diagonal matrix.
• the method further includes performing an inverse-transform to the correction signal by additionally using the scaling diagonal matrix.
• the correction signal includes an optimal coefficient value which minimizes a sum of a distortion component and a rate component.
• the multiple diagonal matrices is read before decoding frames of the video signal.
• Another embodiment of the present invention provides an apparatus of encoding a video signal, comprising: a receiving unit configured to receive an original video signal; an optimizer configured to compare the original video signal with a previously reconstructed signal, and generate a correction signal to minimize a sum of a distortion component and a rate component; and an entropy-encoding unit conifgured to entropy- encode the correction signal that is transmitted to a decoder for video signal reconstruction, wherein the previously reconstructed signal has been inverse- transformed by additionally using a scaling diagonal matrix.
• the optimizer further configurs to calculate an optimal set of multiple diagonal matrices including the scaling diagonal matrix, wherein the correction signal is generated based on the optimal set of multiple diagonal matrices.
• Another embodiment of the present invention provides an apparatus of decoding a video signal, comprising: a receiving unit configured to receive the video signal including a correction signal, and read side information including multiple diagonal matrices from the video signal; an entropy- decoding unit configured to obtain the correction signal by entropy-decoding the video signal; and a reconstruction unit configured to reconstruct a signal based on the correction signal and the multiple diagonal matrices.
• the decoding apparatus further comprises an inverse-transform unit configured to performe an inverse-transform to the correction signal by additionally using a scaling diagonal matrix.
• FIGS. 1 and 2 illustrate schematic block diagrams of an encoder and a decoder in which media coding is performed.
• the encoder 100 of FIG. 1 includes a transform unit 110, a quantization unit 120, a dequantization unit 130, an inverse transform unit 140, a buffer 150, a prediction unit 160, and an entropy encoding unit 170.
• the decoder 200 of FIG. 2 includes an entropy decoding unit 210, a dequantization unit 220, an inverse transform unit 230, a buffer 240, and a prediction unit 250.
• the encoder 100 receives the original video signal and generates a prediction error by subtracting a predicted signal, output by the prediction unit 160, from the original video signal.
• the generated prediction error is transmitted to the transform unit 110.
• the transform unit 110 generates a transform coefficient by applying a transform scheme to the prediction error.
• the transform scheme may include, a block-based transform method and an image-based transform method, for example.
• the block-based transform method may include, for example, Discrete Cosine Transform (DCT) and Karhuhen-Loeve Transform.
• the DCT means that a signal on a space domain is decomposed into two-dimensional frequency components. A pattern having lower frequency components toward an upper left corner within a block and higher frequency components toward a lower right corner within the block is formed. For example, only one of 64 two-dimensional frequency components that is placed at the top left corner may be a Direct Current (DC) component and may have a frequency of 0. The remaining frequency components may be Alternate Current (AC) components and may include 63 frequency components from the lowest frequency component to higher frequency components.
• To perform the DCT includes calculating the size of each of base components (e.g., 64 basic pattern components) included in a block of the original video signal, the size of the base component is a discrete cosine transform coefficient.
• the DCT is transform used for a simple expression into the original video signal components.
• the original video signal is fully reconstructed from frequency components upon inverse transform. That is, only a method of representing video is changed, and all the pieces of information included in the original video in addition to redundant information are preserved. If DCT is performed on the original video signal, DCT coefficients are crowded at a value close to 0 unlike in the amplitude distribution of the original video signal. Accordingly, a high compression effect can be obtained using the DCT coefficients.
• the quantization unit 120 quantizes the generated transform coefficient and sends the quantized coefficient to the entropy encoding unit 170.
• the entropy encoding unit 170 performs entropy coding on the quantized signal and outputs an entropy-coded signal.
• the quantization unit 120 maps a specific range of input values for input data to a single representative value. Quantization may be computed by dividing the input data by a quantization step size as in the following equation 1.
• Equation 1 Y denotes quantized data, X denotes input data, and Q denotes a quantization step size.
• a function Sign() is operation for obtaining the sign of data, and a function Round () denotes round-off operation.
• the quantization step size may be represented by a quantization range. Furthermore, in this specification, the quantization step size may mean a scaling parameter. When video coding is performed, a quantization step size may be changed. A compression ration may be controlled using the changed quantization step size. Meanwhile, a quantization ' parameter using an integer value may be use instead of the quantization step size.
• a quantized coefficient C may be obtained by dividing an input transform coefficient C by a quantization step size Q.
• Equation 2 C denotes a quantized coefficient, C denotes an input transform coefficient, and Q denotes a quantization step size.
• the quantized signal output by the quantization unit 120 may be used to generate a prediction signal.
• the dequantization unit 130 and the inverse transform unit 140 within the loop of the encoder 100 may perform dequantization and inverse transform on the quantized signal so that the quantized signal is reconstructed into a prediction error.
• a reconstructed signal may be generated by adding the reconstructed prediction error to a prediction signal output by the prediction unit 160.
• the buffer 150 stores the reconstructed signal for the future reference of the prediction unit 160.
• the prediction unit 160 generates a prediction signal using a previously reconstructed signal stored in the buffer 150.
• the decoder 200 of FIG. 2 receives a signal output by the encoder 100 of FIG. 1.
• the entropy decoding unit 210 performs entropy decoding on the received signal.
• the dequantization unit 220 obtains a transform coefficient from the entropy- decoded signal based on information about a quantization step size.
• the inverse transform unit 230 obtains a prediction error by performing inverse transform on the transform coefficient.
• a reconstructed signal is generated by adding the obtained prediction error to a prediction signal output by the prediction unit 250.
• the dequantization unit 220 may compute reconstructed data by multiplying quantized data by a dequantization scaling value Q as in the following equation 3.
• Equation 3 X' denotes reconstructed data, Y denotes quantized data, and Q denotes a dequantization scaling value.
• the dequantization scaling value Q may have the same value as a quantization step size.
• the buffer 240 stores the reconstructed signal for the future reference of the prediction unit 250.
• the prediction unit 250 generates a prediction signal using a previously reconstructed signal stored in the buffer 240.
• the present invention provides an intra prediction method in a hybrid video coder.
• Sample values to be compressed are predicted using previously coded context values, and predicted errors are transform-coded. Such a process may be performed on a Gaussian signal so that it has an optimized RD value.
• Common video signals include many signals not suitable for Gaussian signals. Accordingly, the present invention is targeted to such signals and proposes a technology for non-casually predicting each sample using a transform-coded sample and a context value together with a prediction sample.
• Such non- causal encoding may be represented by non-orthogonal transform including a form and parameters.
• FIGS. 3 and 4 illustrate embodiments to which the present invention may be applied and are schematic block diagrams of an encoder and a decoder to which an advanced coding method has been applied.
• the encoder 300 of FIG. 3 includes an optimizer (310) , a quantization unit 315, an inverse transform unit 320, a prediction unit 330, a reconstruction unit 340, a buffer 350, and an entropy encoding unit 360.
• the decoder 400 of FIG. 4 includes an entropy decoding unit 410, a dequantization unit 420, an inverse transform unit 430, a reconstruction unit 440, a buffer 450, and a prediction unit 460.
• the optimizer 310 may fetch at least one of information about the pixels of a current block, information about the pixels of a previously decoded block, and information about a quantization step size from the buffer 350.
• the pixel information of the current block may be indicative of the pixels of a block to be coded that are arranged into a vector.
• the pixel information of a previously decoded block may be indicative of the pixels of a previously decoded block that are arranged into a vector.
• the quantization step size information may be indicative of a quantization step size arranged into a vector.
• the optimizer 310 may obtain a transform coefficient C(i,j) based on at least one of the pixel information of the current block, the pixel information of the previously decoded block, and the quantization step size information.
• the transform coefficient C(i,j) may mean a dequantized transform coefficient .
• the inverse transform unit 320 may receive the obtained transform coefficient C(i,j) and perform inverse transform on the received transform coefficient C(i,j).
• the inverse transform unit 320 may obtain a residual signal "res(i,j)" by performing inverse transform on the received transform coefficient C(i,j) .
• the prediction unit 330 may fetch information about the pixels of the previously decoded block from the buffer 350.
• the prediction unit 330 may predict the pixels of a current layer using at least one of the pixels of the previously decoded block and pixels reconstructed from a previous layer.
• the prediction unit 330 may obtain a prediction signal "pred(i,j)" by performing such prediction.
• the pixels reconstructed from the previous layer may be indicative of the reconstructed pixels of all the previous layers L x , L k- i. This is described in more detail with reference to FIGS. 5 and 6.
• the reconstruction unit 340 may obtain a reconstructed signal "rec(i,j)" by adding the prediction signal “pred(i,j)” obtained by the prediction unit 330 and the residual signal “res(i,j)” obtained by the inverse transform unit 320.
• the reconstructed signal "rec(i,j)” may mean the reconstructed signal of the current layer L k .
• the reconstructed signal "rec(i,j)" is transmitted to the buffer 350 for the future prediction of a next layer.
• the transform coefficient C(i,j) obtained by the optimizer 310 is transmitted to a quantization unit 315.
• the quantization unit 315 performs a quantization process and transmits quantized transform coefficient to the entropy encoding unit 360.
• the transform coefficient C(i,j) may mean a Rate Distortion (RD) -optimized transform coefficient.
• the quantization process may be performed by dividing the transform coefficient C(i,j) by the quantization step size.
• the entropy encoding unit 360 may receive the quantized transform coefficient and perform entropy encoding on the received transform coefficient.
• the decoder 400 of FIG. 4 may receive a signal output by the encoder 300 of FIG. 3.
• the entropy decoding unit 410 may receive a bit stream and perform entropy decoding on the bit stream.
• the dequantization unit 420 may obtain a transform coefficient from the entropy-decoded signal using quantization step size information.
• the inverse transform unit 430 may obtain the residual signal "res(i,j)" by performing inverse transform on the transform coefficient.
• the reconstruction unit 440 may obtain the reconstructed signal "rec(i,j)” by adding the residual signal “res(i,j)” and the prediction signal “pred(i,j)” obtained by the prediction unit 450.
• the reconstructed signal “rec(i,j)” may be transmitted to the buffer 450 and stored therein. Furthermore, the reconstructed signal “rec(i,j)” may be transmitted to the prediction unit 450 for the future prediction of a next signal.
• the embodiments described with reference to the encoder 300 of FIG. 3 may be applied to the operations of the elements of the decoder 400 of FIG. 4.
• a hybrid video coder to which the present invention may be applied performs efficient predictive coding by spatially predicting samples using previously decoded samples (i.e., context values) and performing transform coding on predicted errors .
• block transform is consecutively performed on even signals whose block transform has been partially optimized.
• the partially optimized signals may include signals having significant inter-block correlations and signals having edge and different directional singularities.
• a spatial prediction operation may be considered to be less adaptive to an elaborate prediction process because it generates a prediction signal more adaptive to simple transform compression. Efficiency of such a prediction operation may be strongly dependent on basic processes having a Gaussian signal because the prediction operation is performed using context values.
• x includes a series of horizontal or directional pixels from a target block on which directional prediction is to be performed using a context sample x 0 .
• the context sample x 0 may be obtained from the boundary of a previously decoded block.
• the context sample x 0 is assumed to be available in both an encoder and a decoder. Assuming that linear prediction of Xi using the context sample Xo is Pi(x 0 ) , a residual signal "r ⁇ " may be defined as in the following equation 4.
• the residual signal "r ⁇ " may be represented as in the following equation 5 after it is subjected to transform coding according to a coding process, subjected to transform decoding according to a decoding process.
• Equation 5 x ⁇ denotes a reconstructed signal.
• a prediction method may be further improved using a better predictor using all the decoded information during a decoding process.
• the present invention may have an excellent effect for a video signal having an edge and directional structure.
• the decoder may have access to all of the residual samples. However, it only uses x 0 and r ⁇ when decoding the 1 th sample, In particular, when decoding x i+1 , the decoder has already reconstructed x ⁇ , which is typically a far better predictor of x i+1 compared to xo .
• the decoding chain may be designed as following equation 6.
• this chain and the augmented predictor P t may be feasible.
• the corresponding encoding chain can be described as the selection of optimal coded transform coefficients' which, when fed into the transform decoder in equation 6, result in x that has the minimum distortion at a given target bit-rate.
• the present invention can be generalized to nonlinear prediction functions, it will keep the computationally simple, linear predictors but accomplish prediction using the closest available samples rather than using xo everywhere.
• the present invention can construct equation 7.
• the prediction may be linear with a prediction weight of unity. In this setting, the prediction
• the equation 7 resembles a first-order DPCM decoder that is operating with a prediction weight of unity. While a DPCM system will encode the residuals causally and independently, the decoder of equation 7 corresponds to decoding of residuals that have been encoded non-causally and jointly. This is due to r being the output of the transform decoder shown in equation 6. It can be said that the proposed system gains the prediction accuracy of a DPCM system while exploiting residual dependencies and other DPCM R-D inefficiencies via transform coding.
• Equation 7 can lead to the matrix equation 8.
• F is a (N x N ) lower triangular prediction matrix with equation 9.
• This embodiment is a (N x 1) matrix with unit entries.
• Augmenting equation 8 to accommodate transform coding the present invention can result in equation 10.
• T (N x N ) is the transform used in compression (e.g., the block DCT/DST in HEVC) and c are the de- quantized transform coefficients.
• G FT
• equation 10 corresponds to the transform coding of x - Bx 0 with the non- orthogonal transform G via equation 11.
• the present invention maybe the transform compression of x - Bx 0 using the non- orthogonal transform G.
• the proposed decoding chain can be incorporated within a baseline hybrid codec like HEVC by designing F and B matrices and deriving the equivalent non-orthogonal transform G for each prediction mode.
• Such a decoding chain will have only a marginal complexity increase compared to the baseline since all it will do is predict using the closest samples rather than the boundary samples.
• the encoding chain is more complex, however, because it must pick optimal coefficients to transmit for the decoding chain.
• the present invention will provide an iterative quantization algorithm which the encoder must carry out and derive rate-distortion optimal quantization parameters .
• FIGS. 5 and 6 illustrate embodiments to which the present invention may be applied and define layers illustrating a method of performing prediction using previously coded pixels.
• An embodiment of the present invention provides a method of non-casually predicting a sample using previously coded pixels.
• the pixels of a current block and previously coded pixels used for prediction may be determined using various methods.
• a current block may be decomposed in at least one layer unit. Accordingly, the previously coded pixels may be determined in each layer unit .
• the layer unit may be variously defined based on placed pixels according to a specific criterion.
• pixels arranged in horizontal and vertical directions based on pixels placed at the left top of a current block may be defined as a single layer.
• pixels arranged in the diagonal direction of a pixel placed at the left top may be defined as consecutive layers.
• the layer may be defined as one pixel or a plurality of pixels or may be defined as all the pixels of a block. Furthermore, the layer may be defined as a set of consecutive pixels as illustrated in FIG. 5, but may be defined as a set of pixels that are not consecutive according to circumstances.
• a current block is a BxB block and the position of a pixel within the block is (i,j) .
• ie ⁇ l,2, ... , B ⁇ , j ⁇ l,2, ... , B ⁇ .
• pixels arranged in horizontal and vertical directions based on a pixel placed at the left top of the current block may be defined as a layer Li. That is, a pixel placed at pixel positions (l,j) and (i,l) may be defined as the layer Li .
• previously coded pixels may include the pixels of a layer that is coded right before a layer to be coded.
• a layer L k-1 coded right before the current layer L k may be used.
• pixels neighboring the boundary of the current block may also be used. That is, pixels that neighbor an already decoded block neighboring the current block may be used to predict the layer L k .
• the current layer L k may be predicted based on the reconstructed pixels of all the previous layers L 1( i and pixels that neighboring an already decoded block.
• Another embodiments of the present invention can provide prediction formation.
• the encoder can arrange coeffs(i,j), ie ⁇ l,2, ... , B ⁇ , j € ⁇ l,2, ... , B ⁇ into a vector c. It can be represented as equation 12.
• the encoder can arrange res(i,j), ie ⁇ l,2, ... , B ⁇ , j € ⁇ l,2, ... , B ⁇ into a vector r. It can be represented as equation 13.
• the encoder can arrange pixels from previously decoded blocks into a vector y.
• the present invention can be implemented using matrix multiplication as equation 14.
• the present invention can be implemented using matrix multiplication as equation 15.
• the present invention can be implemented using matrix multiplication as equation 16.
• the present invention can be implemented using matrix multiplication as equation 17.
• FIGS. 5 and 6 may be applied to intra prediction and may also be applied to various prediction modes for intra prediction.
• the present invention is not limited thereto.
• the embodiments may also be applied to inter prediction.
• FIG. 7 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a method of performing prediction using previously coded pixels for each layer.
• an entropy-coded coefficient may be extracted from a received bit stream.
• Entropy decoding may be performed on the entropy-coded coefficient at step S710 and the entropy- decoded coefficient may be dequantized at step S720, thereby being capable of obtaining a transform coefficient "coeffs (i, j ) " .
• a residual signal "res(i,j)” may be obtained by performing inverse transform on the transform coefficient at step S730.
• the residual signal "res(i,j)” is used to reconstruct a current layer L k .
• the pixels of a previously decoded block may be used.
• the pixels of the current layer L k may be predicted using the reconstructed pixels of all the previous layers L i# L k-1 together at step S740.
• a prediction signal "pred(i,j)" generated at step S740 may be added to the residual signal “res(i,j)” obtained at step S730, thereby being capable of reconstructing the pixels of the current layer L k at step S750.
• a reconstructed signal "rec(i,j)” generated as described above may be used to predict a next layer.
• FIG. 8 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a quantization process for obtaining an optimized coefficient.
• the present invention provides a compression method with non-orthogonal transforms.
• c (N x 1) are the transform coefficients.
• Equation 21 hence may be derived.
• Equation 21 can- be recognized as a lattice quantizer whose optimal solution in terms of L requires solving an integer problem. Many suboptimal techniques have been proposed for the solution of equation 19. In order to accommodate fast solutions, the present invention can incorporate a method similar to where one iteratively solves scalar quantization problems concentrating on each coefficient in turn. Assume all coefficients except for the th
• the error vector can be defined as equation 22.
• the distortion may be any integer constraint.
• the optimal quantized coefficient can be obtained as equation 24.
• the encoder may perform repetitive simulations in order to obtain an optimized coefficient to be transmitted to the decoder at step S810.
• the current coefficient may be determined to be an optimized coefficient. For example, assuming that the current coefficient is C n and the previous coefficient is C n -i, whether a difference value C n-1 - C n between the current coefficient and the previous coefficient converges on 0 may be checked at step S820. If, as a result of the check, the difference value C n -i - C n is found to converge on 0, the current coefficient C n may be determined to be an optimized coefficient and transmitted to the decoder at step S830. If, as a result of the check, the difference value C n _i - C n is found to not converge on 0, the current coefficient C n may be returned so that the previous steps S810 and S820 are repeatedly performed.
• an optimized coefficient may be determined by comparing the difference value C n- i - C n between the current coefficient and the previous coefficient with a specific threshold ⁇ . For example, if, as a result of the comparison, the difference value C n- i - C n is found to be greater than the specific threshold ⁇ , the current coefficient C n may be returned so that the previous steps S810 and S820 are repeatedly performed. In contrast, if, as a result of the comparison, the difference value C n _i - C n is found to be equal to or smaller than the specific threshold ⁇ , the current coefficient C n may be determined to be an optimized coefficient and transmitted to the decoder.
• Such an operation may be performed by the encoder of FIG. 3.
• the operation may be performed by the optimizer 310.
• FIG. 9 illustrates an embodiment to which the present invention may be applied and is a detailed flowchart illustrating a quantization process for obtaining an optimized coefficient .
• the encoder may obtain an optimized coefficient based on at least one of information about the pixels of a current block, information about the pixels of a previously decoded block, and information about a quantization step size. Such an operation may be performed by the quantization unit of the encoder.
• the encoder may obtain an initially quantized coefficient based on information about the pixels of a current block and information about the pixels of a previously decoded block at step S910.
• the initially quantized coefficient may be represented as in equation 25.
• C 0 denotes an initially quantized coefficient
• x denotes information about the pixels of a current block
• y denotes information about the pixels of a previously decoded block.
• G H denotes matrices optimized on training sets.
• the matrix G may be indicative of a non-orthogonal transform matrix.
• An error vector indicative of a difference between the original signal and a reconstructed signal may be obtained based on the initially quantized coefficient at step S920.
• the pixel information x of the current block and the pixel information y of the previously decoded block may be used, which may be represented as in equation 26. [Equation 26]
• a temporary vector may be defined as in equation 27.
• t denotes a temporary vector
• g k denotes k th column vector of a matrix G.
• C n-1 (k) denotes a (n-l) th quantized coefficient.
• An n th quantized coefficient C n may be obtained based on the temporary vector t and quantization step size information X(k) at step S930.
• equation 28 may be used.
• X(k) denotes a quantization step size that is to be used for a k th transform coefficient.
• error vector e n may be updated as in equation 29 at step S940.
• n th quantized coefficient C n is obtained through such a process, whether a specific condition is satisfied may , 0 be checked by comparing the n h quantized coefficient C n with the previous coefficient C n- i.
• the n th quantized coefficient C n may be determined to be an optimized coefficient based on a result of the comparison. For example, whether a difference value C n _i - C n between the n th quantized coefficient C n and the previous coefficient C n- i converges on 9 may be checked at step S950.
• the n th quantized coefficient C n may be determined to be an optimized coefficient and transmitted to the decoder at step S960.
• the difference value C n -i - C n is found to not converge on 0, the n th quantized coefficient C n may be returned so that the previous steps are iterated.
• an optimized coefficient may be determined by comparing a difference value Cn-i - C n between a current coefficient and a previous coefficient with a specific threshold ⁇ . For example, this may be represented as in equation 30.
• the current coefficient C n may be returned so that previous steps are iterated.
• the difference value II C n - C n- i H 2 is equal to or smaller than the specific threshold ⁇ , the current coefficient C n may be determined to be an optimized coefficient and transmitted to the decoder.
• FIG. 10 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a process of obtaining an optimized quantization step size.
• an optimized quantization step size may be derived in a process of performing, by the encoder, quantization in order to obtain an optimized coefficient.
• quantization step size information may be obtained from a quantization parameter value at step S1010.
• the quantization step size information may be represented as in equation 31.
• equation 31 A(k) denotes a k th quantization step size, and QP denotes a quantization parameter.
• Matrices and a vector to be used to obtain an optimized coefficient may be initialized at step S1020.
• the vector and the matrices may be represented as in equations 32 and 33.
• the optimizer may obtain an optimized quantization step size based on the k th quantization step size A(k) and the initialized vector u(k) and matrices G (k, l), H(k, l) at step S1030.
• a convex optimization algorithm may be used.
• An embodiment of the present invention can provide a method of deriving optimal quantizer step-sizes.
• Rate-Distortion optimal design of quantizer step- sizes is in general a difficult problem since tractable expressions for rate and distortion are codec dependent and hard to obtain.
• the high rate approximations can be used in order to optimize the vector of step-sizes, ⁇ .
• H() denotes entropy. Since coefficient Ci is scalar quantized using the step-size ⁇ i, the approximation can be invoked at high bit-rates.
• Equation 35 h(Ci) is the differential entropy of the continuously valued coefficient.
• equation 36 may be needed.
• equation 37 can be obtained.
• V(X) TT ⁇ GE[ ⁇ C-C) ⁇ C-C) T ⁇ G T )
• Equation 39 leads to the rounding error satisfying
• Equation 42 can be obta
• Equation 42 Considering the diagonal elements of Equation 42 may lead to Equation 43.
• Equations 38 and 43 become equation 44.
• Equation 46 ⁇ is a Lagrange multiplier. Optimization of equation 46 yields the following equation 47.
• FIGS. 11 and 12 illustrate embodiments to which the present invention may be applied, wherein FIG. 11 illustrates test images to which the present invention has been applied and FIG. 12 illustrates percentages of rate gains to test images .
• a signal having an edge and directional structure can be coded more efficiently by non-casually predicting a video signal using a transform-coded signal along with a predicted signal.
• intra prediction was performed on a layer of a 1-pixel thickness within a block, and the prediction process and the quantization process described with reference to FIGS . 3 to 10 were applied to the simulation.
• FIG. 11 illustrates 6 test images (a) -(f), and each of the 6 images has an image feature .
• Each of the 6 test images may be considered to correspond to a signal in which at least one of an edge and directional singularity significantly appears compared to other common images .
• results such as those of FIG. 12(a), can be found.
• FIGS. 11(a), 11(b), and 11(e) have significant directional singularities compared to the remaining images FIGS. 11(c), 11(d), and 11(f).
• FIGS. 11(a), 11(b), and 11(e) have relatively higher rate gains .
• FIG. 13 illustrates an embodiment to which the present invention may be applied and is a schematic flowchart illustrating an improved predictive coding method.
• the encoder may compare the original video signal with available reconstructed signals at step S1320. And, the encoder may determine a correction signal based on a result of the comparison.
• the correction signal may be determined to minimize a sum of a distortion component and a rate component.
• the distortion component is indicative of total distortion between the original video signal and the correction signal
• the rate component is indicative of a number of bits required to send the transform-coded correction signal.
• the encoder may perform decoding simulations.
• the encoder may generate a transform-coded correction signal based on a result of the comparison at step S1330.
• the encoder may generate a prediction signal based on the transform-coded correction signal and the available reconstructed signals at step S1340.
• the encoder may reconstruct a signal by adding the transform-coded correction signal to the prediction signal at step S1350.
• FIG. 1 illustrates an embodiment to which the present invention may be applied and is a schematic flowchart illustrating a method of performing quantization based on an optimized quantization step size.
• An embodiment of the present invention provides a method of deriving an optimized quantization step size in a process of performing quantization in order to obtain an optimized coefficient. Quantization may be performed based on the derived quantization step size.
• information about a quantization step size may be obtained from a quantization parameter value.
• the quantization step size information may mean a scaling parameter.
• the scaling parameter may be obtained using a Rate
• the scaling parameter may be determined to be a value that minimizes the sum of a distortion component and a rate component at step S1410.
• a transform-coded correction signal may be obtained according to the embodiments described above with reference to FIGS. 8 to 10.
• the transform-coded correction signal may include an optimized transform coefficient.
• quantization may be performed on the transform-coded correction signal based on the scaling parameter determined at step S1410.
• the quantized coefficient may be subjected to entropy encoding and transmitted at step S1430.
• FIGS. 15 and 16 illustrate embodiments to which the present invention may be applied and are schematic block diagrams of an encoder and a decoder to which an advanced coding method has been applied through control of a quantization error.
• the present invention defines a set of coding parameter to control quantization effects by manipulating factors simultaneously in three spaces: spatial, spectral, and lattice norm. Improved compression may be provided by finding optimized parameters determined using a specific type and training technology of an image compression method.
• Predictive coding is based on that a signal element is predicted using a previously coded part and a difference value between a predicted value and an actual value is coded.
• An N- dimensional vector X is used to indicate coded data (e.g., an image or video frame)
• a vector P is used to indicate a value predicted from the N-dimensional vector X.
• Such prediction is performed using a vector y formed from the past values of a reconstructed vector X.
• a difference vector indicative of a prediction residual may be computed as in the following equation 48.
• such a difference is additionally transformed using orthogonal linear transform represented by an NxN matrix T. Thereafter, a vector coefficient is converted into an integer for entropy coding.
• a vector having an integer coefficient is indicated by c and may be defined as in the following equation 49.
• quantization is performed using an orthogonal scaling matrix Q and may be defined as in the following equation 50.
• the reconstructed vector X may be computed by both the encoder and the decoder using the following equation 52.
• Equation 52 X denotes a reconstructed vector, p denotes a prediction vector, T denotes a transform matrix, Q denotes a quantization matrix, and c denotes a transform coefficient. 5Q
• the distribution of quantization errors in a frequency domain may be changed using different values of a diagonal matrix Q.
• All the elements within the vector of an image or video block may not be used in the same way when inter block prediction is performed. Accordingly, prediction precision may be significantly reduced due to the errors of some elements present at the boundary of a block.
• a blocking artifact may be generated at the boundary of a block.
• the encoder 1500 to which the present invention may be applied may include an optimizer 1520, a dequantization unit 1530, an inverse transform unit 1540, a buffer 1550, a prediction unit 1560, and an entropy encoding unit 1570.
• the inverse transform unit 1540 may include a spatial scaling unit 1545.
• the optimizer 1520 may obtain an optimally quantized transform coefficient.
• the optimizer 1520 may obtain an optimally quantized transform coefficient through a training step. For example, the optimizer 1520 may compute an optimized set of diagonal matrices S, W, and Q from a viewpoint of Rate Distortion (RD) .
• RD Rate Distortion
• An embodiment of the present invention provides a method of adding another diagonal matrix S, that is, a scaling factor on a space domain.
• a process for reconstructing a signal may be changed as in the following equation 53.
• an optimized transform coefficient may be calculated based on the following equation 54.
• Equation 54 W denotes another diagonal matrix used to differentiate the importance of errors in the spatial domain.
• objective distortion measurement such as a Mean Squared Error (MSE)
• MSE Mean Squared Error
• another distortion measurement including subjective factors, such as the visibility of blocking artifacts may be used.
• the values of diagonal matrices S, W, and Q may be encoded.
• a proper protocol that may be recognized by the decoder may be used.
• the dequantization unit 1530 may obtain a transform coefficient by performing dequantization on the optimally quantized transform coefficient.
• the inverse transform unit 1540 may obtain a predicted error vector by performing inverse transform on the transform coefficient.
• the inverse transform may include a scale orthogonal matrix S.
• Scaling using the scale orthogonal matrix S may be performed by the spatial scaling unit 1545 of the inverse transform unit 1540. Furthermore, the spatial scaling unit 1545 may be placed after the inverse transform process of the inverse transform unit 1540.
• a reconstructed signal may be generated by adding the obtained predicted error vector to a prediction signal output by the prediction unit 1560.
• the buffer 1550 stores the reconstructed signal for the future reference of the prediction unit 1560.
• the prediction unit 1560 generates a prediction signal using a previously reconstructed signal stored in the buffer 1550.
• the optimally quantized transform coefficient obtained by the optimizer 1520 may be transmitted to the entropy encoding unit 1570.
• the entropy encoding unit 1570 may perform entropy encoding on the optimally quantized transform coefficient and output the resulting transform coefficient.
• the decoder 1600 to which the present invention may be applied may include an entropy decoding unit 1610, a dequantization unit 1620, an inverse transform unit 1630, a buffer 1640, and a prediction unit 1650.
• the inverse transform unit 1630 may include a spatial scaling unit 1635. e .
• the decoder 1600 of FIG. 16 receives a signal output by the encoder 1500 of FIG. 15. The received signal is subjected to entropy decoding through the entropy decoding unit 1610.
• the dequantization unit 1620 obtains a transform coefficient from the entropy-decoded signal using quantization step size information.
• the inverse transform unit 1630 obtains a predicted error by performing inverse transform on the transform coefficient.
• the inverse transform may include a scale orthogonal matrix S.
• Scaling using the scale orthogonal matrix S may be performed by the spatial scaling unit 1635 of the inverse transform unit 1630.
• the spatial scaling unit 1635 may be placed after the inverse transform process of the inverse transform unit 1630. Furthermore, the embodiments described with reference to FIG. 15 may be applied.
• a reconstructed signal is generated by adding the obtained predicted error to a prediction signal output by the prediction unit 1650.
• the buffer 1640 stores the reconstructed signal for the future reference of the prediction unit 1650.
• the prediction unit 1650 may generate a prediction signal using a previously reconstructed signal stored in the buffer 1640.
• FIG. 17 illustrates an embodiment to which the present invention may be applied and is a flowchart illustrating a process of obtaining a scaling diagonal matrix through a Rate Distortion (RD) optimization process.
• RD Rate Distortion
• the present invention can model the approximation using statistical methods, by defining an additive error vector e.
• Equation 56 means that errors have roughly the same distribution for all pixels in a block.
• the elements of e are independent random Gaussian variables, with zero mean and same variance .
• Equation 52 means that now the error in each pixel has different variances, proportional to the scaling factors in diagonal matrix S. Larger values of Si,i thus produce relatively larger error variances, and vice-versa.
• the present invention can be applied for each pre-defined video segment, for example, coding unit, frame, tile, slice, etc.
• the present invention can be performed according to the following steps.
• the encoder can choose the matrices S,W, and Q to be used for coding pixel blocks within the segment.
• the encoder can add to the compressed bitstream the information about matrices S and Q. For example, T is assumed constant, and W is only used by the encoder.
• the encoder can find the 5? optimal vector c Z N , entropy code its value, and add it to the compressed bitstream.
• the present invention can be performed according to the following steps.
• the decoder can read from the compressed bitstream the information about matrices S and Q.
• the decoder can entropy decode the vector c € ⁇ Z N , and compute reconstructed pixel values using equation 59.
• An embodiment of the present invention provides a process of obtaining a scaling diagonal matrix through a Rate Distortion (RD) optimization process.
• RD Rate Distortion
• the encoder may perform an RD optimization process through training at step S1710.
• an RD optimization process may be performed by the optimizer 1520.
• An optimized set of diagonal matrices S, W, and Q may be computed through the RD optimization process at step S1720.
• the values of the diagonal matrices S, W, and Q may be encoded into side information at step S1730. Thereafter, a video signal may be coded or decoded according to the processes described with reference to FIGS. 15 and 16 at step S1740.
• the scaling diagonal matrix S of the diagonal matrices may be used in the inverse transform unit 1540 of the encoder 1500 or the inverse transform unit 1630 of the decoder 1600 so that a quantization is controlled error even on the space domain.
• FIG. 18 illustrates an embodiment to which the present invention may be applied and is a graph illustrating a comparison between the coding gains of respective images in the case in which coding is performed using an optimized scaling matrix and the case in which coding is performed using an existing method.
• FIG. 18 illustrates relations between control of error transfer and coding gains.
• Dotted lines in the graph denote the coding gains of a common codec, and solid lines denote coding gains when optimized diagonal matrices are used.
• the present embodiment corresponds to a case where planar prediction and 4X4 DCT are used. It may be seen that better coding efficiency is obtained when all the optimized diagonal matrices are used in three test images, "Woman”, “Bike”, and “Cafe” . This is only an embodiment of the present invention, and the present invention is not limited to the aforementioned conditions and may be applied to embodiments having other conditions.
• FIGS. 19 and 20 are embodiments to which the present invention may be applied and are schematic block diagrams illustrating an encoder and a decoder to which an advanced coding method may be applied.
• the encoder 1900 of FIG. 19 includes an optimizer 1910, a quantization unit 1920, and an entropy encoding unit 1930.
• the decoder 2000 of FIG. 20 includes an entropy decoding unit 2010, a dequantization unit 2020, an inverse transform unit 2030, and a reconstruction unit 2040.
• the optimizer 1910 obtains an optimized transform-coded correction signal.
• the optimizer 1910 may use the following embodiments in order to obtain the optimized transform-coded correction signal.
• a reconstruction function for reconstructing a signal may be defined as follows.
• Equation 60 x denotes a reconstructed signal, c denotes a decoded transform-coded correction signal, and y . n
• R(c,y) denotes a reconstruction function using c and y in order to generate a reconstructed signal .
• a reconstruction function may be defined as a relationship between previously reconstructed values and a transform-coded correction signal. Accordingly, the decoded correction signal affects not only the reconstruction value, but also the entire reconstruction process and the choice of reconstruction functions.
• a correction signal may be defined as follows .
• Equation 61 e denotes a correction signal, c denotes a transform-coded correction signal, and T denotes a transform matrix. Also, in some cases, the correction signal may mean error signal or prediction error signal.
• a reconstructed signal may be defined as follows .
• Equation 62 x n denotes an n th component of the reconstructed signal, e denotes the correction signal, and y denotes a context signal.
• R n denotes a reconstruction function using e, y and x in order to generate a reconstructed signal.
• the reconstruction function R n may be defined as follows.
• P n denotes a type of prediction function formed of the parameters in order to generate a prediction signal.
• the prediction function may be, for example, a median function, a combination of a rank order filter and a nonlinear function, or a combination of linear functions. Furthermore, each of the non-linear prediction function P n () may be a different non-linear function.
• a quantization unit 1920 may be included in the optimizer 1910, or the optimizer 1910 may include transform unit.
• the encoder 1900 and the decoder 2000 may include a storage unit of candidate functions for selecting the non-linear prediction function.
• the optimized non- linear prediction function may be selected from candidate functions stored in the storage unit.
• the optimizer 1910 may generate an optimized prediction signal using the optimized non- linear prediction function. And, the optimizer 1910 may generate an optimized prediction error signal based on the optimized prediction signal, and may perform transform coding on the optimized prediction error signal. The optimizer 1910 may output a transform-coded coefficient through the transform coding. In this case, the transform-coded coefficient may mean an optimized transform coefficient.
• the output transform coefficient is transmitted to the quantization unit 1920.
• the quantization unit 1920 quantizes the transform coefficient and sends the quantized transform coefficient to the entropy encoding unit 1930.
• the entropy encoding unit 1930 may perform entropy encoding on the quantized transform coefficient and output a compressed bit stream.
• the decoder 2000 of FIG. 20 may receive the compressed bit stream from the encoder of FIG. 19, may perform entropy decoding through the entropy decoding unit 2010, and may perform dequantization through the dequantization unit 2020.
• a signal output by the dequantization unit 2020 may mean an optimized transform coefficient.
• the inverse transform unit 2030 receives the optimized transform coefficient, performs an inverse transform process, and may obtain a prediction error signal through the inverse transform process.
• the reconstruction unit 2040 may obtain a reconstructed signal by adding the prediction error signal and a prediction signal together. In this case, various embodiments described with reference to FIG. 19 may be applied to the prediction signal .
• FIG. 21 is an embodiment to which the present invention may be applied and is a schematic flowchart illustrating an advanced video coding method.
• the encoder may compare the original video signal with available reconstructed signals at step S2120. And, the encoder may determine a correction signal based on a result of the comparison at step S2130.
• the correction signal may be determined to minimize a sum of a distortion component and a rate component.
• the distortion component is indicative of total distortion between the original video signal and the correction signal
• the rate component is indicative of a number of bits required to send the transform-coded correction signal.
• the encoder may perform decoding simulations. This invention may further comprise determining a reconstruction function to be used for the signal reconstruction, and the reconstruction function includes at least one of a linear component and a non- linear component.
• the reconstruction function may be determined based on all the previously reconstructed samples and the correction signal .
• the encoder may generate a transform-coded correction signal to be transmitted for a signal reconstruction at step S2140.
• the transform-coded correction signal may be multiplied by a dequantization matrix and an inverse-transform matrix, and wherein the dequantization matrix may be selected for controlling a bit- rate and quantization errors.
• the transform-coded correction signal may correspond to the correction signal for a group of pictures and a spatiotemporal transform coding may has been applied to the correction signal.
• the decoder may receive a bit stream including a transform- coded correction signal obtained according to the present invention, may perform entropy decoding through the entropy decoding unit, may perform dequantization through the dequantization unit, and may perform inverse transform through the inverse transform unit.
• the decoder may obtain a correction signal by performing inverse- transform to the transform-coded correction signal.
• the decoder may obtain a reconstructed signal using a reconstruction function that combines the obtained correction signal and a context signal.
• the context signal may be obtained based on all previously reconstructed samples .
• the decoder may determine a reconstruction function to be used for the signal reconstruction, and the reconstruction function may include at least one of a linear component and a non- linear component.
• the reconstruction function may be determined based on all the previously reconstructed samples and the correction signal.
• the transform-coded correction signal may be multiplied by a dequantization matrix and an inverse- transform matrix. Also, the transform-coded correction signal may correspond to the correction signal for a group of pictures and a spatiotemporal transform coding has been applied to the correction signal .
• the decoder and the encoder to which the present invention may be applied may be included in a multimedia broadcasting transmission/reception apparatus, a mobile communication terminal, a home cinema video apparatus, a digital cinema video apparatus, a surveillance camera, a video chatting apparatus, a real-time communication apparatus, such as video communication, a mobile streaming apparatus, a storage medium, a camcorder, a VoD service providing apparatus, an Internet streaming service providing apparatus, a three- dimensional (3D) video apparatus, a teleconference video apparatus, and a medical video apparatus and may be used to code video signals and data signals.
• a multimedia broadcasting transmission/reception apparatus a mobile communication terminal, a home cinema video apparatus, a digital cinema video apparatus, a surveillance camera, a video chatting apparatus, a real-time communication apparatus, such as video communication, a mobile streaming apparatus, a storage medium, a camcorder, a VoD service providing apparatus, an Internet streaming service providing apparatus, a three- dimensional (3D) video apparatus, a teleconference video apparatus
• the decoding/encoding method to which the present invention may be applied may be produced in the form of a program that is to be executed by a computer and may be stored in a computer-readable recording medium.
• Multimedia data having a data structure according to the present invention may also be stored in computer-readable recording media.
• the computer-readable recording media include all types of storage devices in which data readable by a computer system is stored.
• the computer-readable recording media may include a BD, a USB, ROM, RAM, CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, for example.
• the computer-readable recording media includes media implemented in the form of carrier waves (e.g., transmission through the Internet) .
• a bit stream generated by the encoding method may be stored in a computer-readable recording medium or may be transmitted over wired/wireless communication networks.

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